2003/07/17 by Ioana Dumitriu, Dumitriu, Ioana, Etienne Rassart +1
Mathematics · #05A19 (Primary) #15A52 #82B41 (Secondary) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications #math.CO #msc:05A19 #msc:15A52 #msc:82B41
paper · pdf · doi:10.48550/arxiv.math/0307252
14 pages, 13 figures and diagrams; submitted to the Electronic Journal of Combinatorics
arxiv created 2003/07/17 · openalex publication_date 2003/07/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish three identities involving Dyck paths and alternating Motzkin paths, whose proofs are based on variants of the same bijection. We interpret these identities in terms of closed random walks on the halfline. We explain how these identities arise from combinatorial interpretations of certain properties of the β-Hermite and β-Laguerre ensembles of random matrix theory. We conclude by presenting two other identities obtained in the same way, for which finding combinatorial proofs is an open problem.